Yes fajitas really are a Mexican food.
However fajitas are also a Texas Food so in reality fajitas are a Tex Mex food which is both Mexican Food and a Texan Food.
Fajitas are a blending of Texas cowboy and also Mexican Panchero Food.
So when you're eating fajitas you're eating both Mexican and Texan Food.
The word Faja means “belt” or “girdle” in English and the Mexican term for grilled skirt steak is arracheras, and its American counterpart is.
Fajitas are usually served warm but you can also eat them cold if you want too as long as you've cooked the ingredients or cooked the Fajita fully.